I've read that a singularity is formed when the increasing gravity of a collapsing star overcomes its increasing density, resulting in an infinitely dense "point" of zero dimensions. But the mathematics seems to say the opposite.
Newton's famous formula for gravitational attraction has d squared in the denominator, where d in this case is the radius of the collapsing star. The formula for density in this case has the radius cubed in the denominator, as the star's volume is a function of the cube of its radius. Thus, as these two denominators shrink as the star collapses, its density grows as the cube of the radius but the gravitational force grows only as the square of the radius.
So how does the star's increasing gravity overcome its more rapidly increasing density?